唐山地震前后京津唐张地区的应力场

作者从断裂力学观点研究了圆盘形纯剪切破裂产生的远场位移,导出了远场位移的解析表达式.用此表达式计算了远场位移脉冲波形及其谱.求得了P波和S波拐角频率F_cα、f_cβ与震源破裂半径的关系式,t_2α和t_2β分别是P波与S波的震源脉冲宽度在震源球上的平均值.V_r是破裂速度,取0.775β,α、β是P波与S波速度.介质吸收的影响,假定在略去路径滞后因子e-（iωr）/c后是最小相移滤波器,应用希尔伯特（Hilbert）变换导出了介质的频率响应公式 式中, r为震源距,c为波速,Q为介质品质因数,ω_m为高频截止频率.它与富特曼（Futterman）公式是不一样的.在考虑了介质吸收影响与仪器频率特性影响后,在频率域中求出了震源尺度2a和地震矩M₀.在时间域中,利用快速傅立叶反变换求出介质和仪器的脉冲响应后与震源脉冲折积,求得了合成地震图,用此图得到了地震图初动半周期T_2P与震源尺度2a或震源脉冲宽度t_2a之间的关系量板.用此量板在时间域中也求得震源尺度2a,与频率域中求得的结果基本一致. 利用从断裂力学观点研究震源破裂过程导出的关系式求出了京津唐张地区的区域剪切应力τ₀,式中η为地震辐射效率,取0.05;v为泊松比,取0.252;μ为刚性模量,取3.3×10¹¹达因/厘米².结果表明,1976年7月28日唐山大震前,唐山-丰南一带应力值最高，达870巴，离开唐山仅100公里左右的昌黎地区的应力就只有200巴左右.唐山大震后，地震破裂带中部的唐山一丰南一带，t₀降至100巴左右，而破裂带两头应力值仍很高，尤其是西南头的宁河一带，达400-500巴.直到11月15日此处发生6.9级强余震后应力值才降到200巴左右.

THE STRESS FIELD OF THE PEKING-TIENTSIN-TANGSHAN-ZHANGJIAKOU AREA BEFORE AND AFTER THE TANGSHAN EARTHQUAKE OF JULY 28, 1976

From the point of view of fracture mechanics, we studied the far displacement field produced by a disk-shaped pure shear fracture and obtained an analytic expression for that field. Then, by using this expression we calculated the form of the impulse and its spectrum and found a relation between the corner frequencies f_cα,f_cβ of the P and 8 waves and the fracturing radius of the earthquake focus, i.e. f_cα = 0.6/t_2α = 0.6/al/vr + π/4α) and f_cβ = 0.45/t_2β = 0.45/a（1/vr + β/4β）, where t_2α and t_2β are respectively the average values on the focal sphere of the impulse widths of the earthquake focus of the P and S waves, v_r is the velocity of fracturing, taking as 0.775 β;α,β are the velocities of the P and 8 waves. In neglecting the delay factor of theray paths e-iwr/c, the effect of the absorption of the media resembles a minimum phase-shift filter. Employing Hilbert Transform, the frequency response .B（w） =exp of the media was found, in which t_*=r/CQ, where r, the distance from the earthquake focus; c, velocity of waves; Q, quality factor of the media and wm, the high cut frequency. This expression is different from that of Futterman. After taking into consideration of the effect of the absorption of the media and the frequency characteristics of the instruments, the earthquake focal dimension 2a and the seismic moment M₀ in the frequency domain were obtained. While in the time domain, fast Fourier Inverse Transform was used to get the impulse response of the media and the instruments and then convolved with the impulse of the earthquake focus to construct the synthetic seismogram. From it we can get the relation between the initial half period T_2P and the dimension 2a or impulse width t_2α of the earthquake focus. Then draw the nomogram for this relation. From the nomogram we can get 2a, the focal dimension. The value is essentially the same as that obtained in the frequency domain.Based on the relation M_s = 21og（2a） +1/1.5, as the outcomeof the study of fracture processes of the earthquake focus in the light of frecture mechanics, we were able to find the regional shear stressτ₀ of the Peking-Tientsin-Tangshan-Zhangjiakou area. Here, η, efficiency of rediation of the earthquake, taking as 0.05: v, Poisson Eatio, taking as 0.252; μ, rigidity modulus, taking as 3.3 10¹¹ dyne/cm². Computations show that before the Tangshan Earthquake of July 28, 1976, the stress value of the Tangshan-Fengnan area was the highest, reaching a value of 870 bars. But in the Changli area, at a distance of about 100 km away, the stress had a value of only 200 bars. After the Tangshan Earthquake, in the Tangshan-Fengnan area, located in the central portion of the earthquake fault zone, τ₀ dropped to 100 bars. However, at both ends of the fault zone, the stress was still very high in value, especially at the southwestern end, in the vicinity of Ninghe, the stress value there was 400-500 bars. Until November 15, 1976, a strong aftershock of magnitude 6.9 occurred here, after which the stress value decreased to 200 bars.